Abstract:The numerical treatment of the hyperbolic system of nonlinear wave equations with linear viscosity, , is studied for a large class of globally Lipschitz continuous functions , including non-monotone stress-strain relations. The analyzed method combines an implicit Euler scheme in time with Courant (continuous and piecewise affine) finite elements in space for general time steps with varying meshes. Explicit a priori error bounds in , , and are established for the solutions of the fully discrete scheme.